Definition 5 ([1]}) 

Let \(G\)  be a group object in \({K}/B\) . A fiberwise principal \(G\)  bundle in \({K}/B\) 
consists of a map \(\pi \colon P\rightarrow M\)  in \({K}/B\)  which admits local sections together with an action of \(G\)  on \(P\) 
which is strongly free in the sense that the diagram
\((-9.5,6.25)*+{P\times _B G}="1";(-9.5,-6.25)*+{P}="2";(9.5,6.25)*+{P}="3";(9.5,-6.25)*+{M}="4";{_-{p_1} "1";"2"};{"1";"3"};{^-{\pi } "3";"4"};{_-{\pi } "2";"4"};\) 
